Question

Наташа и Илья решали примеры на скорость. Каждый из учеников должен был решить 60 примеров. Илья выполнил все задания на минуту раньше, чем Наташа. Одноклассники заметили, что Илья каждую минуту решал на 5 примеров больше Наташи. Сколько примеров в минуту решал Илья?

Answer 1

Ответ:

Пошаговое объяснение:

Решение примеров Наташи в минуту:

60/t.

Решения примеров Ильи в минуту:

60/(t-1)

60/(t-1) +5=60/t

60t-+5t(t-1)=60(t-1)

60t+5t²-5t=60t-60

5t²-5t-60=0

Сократим на 5.

t²-t-12=0

t₁₂= (1±√(1+48))/2=(1±7)/2

t₁=4.

t₂=(1-7)/2=-6/2=-3    -   этот корень не подходит, так как отрицательный.

60/(4-1)=60/3=20.

20+5=25 примеров   в минуту решал Илья.

60/4=15 примеров   в минуту решала Наташа.

Answer 2

Problem Statement

Наташа и Илья решали примеры на скорость. Каждый из учеников должен был решить 60 примеров. Илья выполнил все задания на минуту раньше, чем Наташа. Одноклассники заметили, что Илья каждую минуту решал на 5 примеров больше Наташи. Сколько примеров в минуту решал Илья?

Solution

To find out how many examples Ilya solved per minute, we can set up an equation based on the given information.

Let's assume that Natasha solved x examples per minute. Since Ilya solved 5 more examples per minute than Natasha, he solved x + 5 examples per minute.

We know that both Natasha and Ilya solved a total of 60 examples. Natasha took one minute longer than Ilya to solve all the examples. Therefore, we can set up the following equation:

(x + 5) * (t - 1) = 60

Where: - x is the number of examples Natasha solved per minute - t is the total time taken by Natasha to solve all the examples

Simplifying the equation, we get:

xt - x + 5t - 5 = 60 xt + 5t - x - 5 = 60 xt + 5t - x = 65

Since we don't have the exact values of x and t, we cannot solve this equation directly. However, we can make some observations based on the given information.

We know that both Natasha and Ilya solved a total of 60 examples. Natasha took one minute longer than Ilya to solve all the examples. This means that Ilya took t - 1 minutes to solve all the examples.

Let's assume that Ilya solved y examples per minute. Since Ilya solved 5 more examples per minute than Natasha, we can write:

y = x + 5

Now, we can rewrite the equation as:

y * (t - 1) = 60

Substituting the value of y, we get:

(x + 5) * (t - 1) = 60

This equation is the same as the one we derived earlier. Therefore, we can conclude that the number of examples Ilya solved per minute is equal to the number of examples Natasha solved per minute plus 5.

Therefore, Ilya solved 5 examples per minute.